{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:16:06Z","timestamp":1770909366083,"version":"3.50.1"},"reference-count":44,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001824","name":"Grant Agency of the Czech Republic","doi-asserted-by":"crossref","award":["GA19-12790S"],"award-info":[{"award-number":["GA19-12790S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:p> We deal with the question of the [Formula: see text]-reducibility of pseudovarieties of ordered monoids corresponding to levels of concatenation hierarchies of regular languages. A pseudovariety of ordered monoids [Formula: see text] is called [Formula: see text]-reducible if, given a finite ordered monoid M, for every inequality of pseudowords that is valid in [Formula: see text], there exists an inequality of [Formula: see text]-words that is also valid in [Formula: see text] and has the same \u201cimprint\u201d in M. <\/jats:p><jats:p> Place and Zeitoun have recently proven the decidability of the membership problem for levels [Formula: see text], 1, [Formula: see text] and [Formula: see text] of concatenation hierarchies with level 0 being a finite Boolean algebra of regular languages closed under quotients. The solutions of these membership problems have been found by considering a more general problem of separation of regular languages and its further generalization\u00a0\u2014 a problem of covering. Following the results of Place and Zeitoun, we prove that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels [Formula: see text] and [Formula: see text] are [Formula: see text]-reducible. As a corollary of these results, we obtain that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels [Formula: see text] and [Formula: see text] are definable by [Formula: see text]-inequalities. Furthermore, in the special case of the Straubing\u2013Th\u00e9rien hierarchy, using a characterization theorem for level 2 by Place and Zeitoun, we obtain that the level 2 is definable by [Formula: see text]-identities. <\/jats:p>","DOI":"10.1142\/s0218196724500024","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T14:19:45Z","timestamp":1703686785000},"page":"87-135","source":"Crossref","is-referenced-by-count":2,"title":["The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9828-5458","authenticated-orcid":false,"given":"Jana","family":"Vola\u0159\u00edkov\u00e1","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Masaryk University, Kotl\u00e1\u0159sk\u00e1 2, 611 37 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"key":"S0218196724500024BIB001","volume-title":"Finite Semigroups and Universal Algebra","author":"Almeida J.","year":"1994"},{"key":"S0218196724500024BIB002","first-page":"531","volume":"54","author":"Almeida J.","year":"1999","journal-title":"Publ. Math. Debrecen"},{"key":"S0218196724500024BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-21500-6_4"},{"key":"S0218196724500024BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671540010X"},{"key":"S0218196724500024BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196716500648"},{"key":"S0218196724500024BIB006","doi-asserted-by":"publisher","DOI":"10.1515\/forum-2016-0028"},{"key":"S0218196724500024BIB007","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611500012144"},{"key":"S0218196724500024BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0039607"},{"key":"S0218196724500024BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02930-1_10"},{"key":"S0218196724500024BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2011.10.022"},{"key":"S0218196724500024BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(71)80003-X"},{"key":"S0218196724500024BIB012","volume-title":"Automata, Languages and Machines","author":"Eilenberg S.","year":"1974"},{"key":"S0218196724500024BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2003.10.034"},{"key":"S0218196724500024BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2019.03.020"},{"key":"S0218196724500024BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(95)00223-J"},{"key":"S0218196724500024BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(88)90042-4"},{"key":"S0218196724500024BIB017","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1965-0188316-1"},{"key":"S0218196724500024BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0028813"},{"key":"S0218196724500024BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/BF01225473"},{"key":"S0218196724500024BIB020","first-page":"80","volume":"39","author":"Pin J.-\u00c9.","year":"1995","journal-title":"Russ. Math. (Izvestija vuzov. Matematika)"},{"key":"S0218196724500024BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59136-5_10"},{"key":"S0218196724500024BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00230-4"},{"key":"S0218196724500024BIB023","series-title":"Leibniz International Proceedings in Informatics","first-page":"31","volume-title":"Proc. Symp. Theoretical Aspects of Computer Science (STACS 09)","volume":"2","author":"Pin J.-\u00c9.","year":"2009"},{"key":"S0218196724500024BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/BF01243597"},{"key":"S0218196724500024BIB025","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.0192"},{"key":"S0218196724500024BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/BF02679467"},{"key":"S0218196724500024BIB027","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2015.28"},{"issue":"4","key":"S0218196724500024BIB028","first-page":"1","volume":"14","author":"Place T.","year":"2018","journal-title":"Log. Methods Comput. Sci."},{"key":"S0218196724500024BIB029","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-43951-7_29"},{"issue":"3","key":"S0218196724500024BIB030","first-page":"1","volume":"14","author":"Place T.","year":"2018","journal-title":"Log. Methods Comput. Sci."},{"key":"S0218196724500024BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-018-9867-0"},{"key":"S0218196724500024BIB032","doi-asserted-by":"publisher","DOI":"10.1145\/3303991"},{"key":"S0218196724500024BIB033","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2019.8785655"},{"key":"S0218196724500024BIB034","doi-asserted-by":"publisher","DOI":"10.1145\/3356339"},{"issue":"3","key":"S0218196724500024BIB035","first-page":"24:1","volume":"17","author":"Place T.","year":"2021","journal-title":"Log. Methods Comput. Sci."},{"key":"S0218196724500024BIB036","doi-asserted-by":"publisher","DOI":"10.1142\/9789812776884_0017"},{"key":"S0218196724500024BIB037","doi-asserted-by":"publisher","DOI":"10.1007\/BF02483902"},{"key":"S0218196724500024BIB038","doi-asserted-by":"publisher","DOI":"10.1007\/b104443"},{"key":"S0218196724500024BIB039","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90108-7"},{"key":"S0218196724500024BIB040","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-07407-4_23"},{"key":"S0218196724500024BIB041","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(81)90036-0"},{"key":"S0218196724500024BIB042","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(85)90062-3"},{"key":"S0218196724500024BIB043","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(81)90057-8"},{"key":"S0218196724500024BIB044","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(82)90016-2"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196724500024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T02:23:59Z","timestamp":1710123839000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196724500024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2]]},"references-count":44,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["10.1142\/S0218196724500024"],"URL":"https:\/\/doi.org\/10.1142\/s0218196724500024","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2]]}}}